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The table shows a bacterial population y after x days.
Day, x
0
1
2
3
4
Population, y 5 35 245 1715 12,005
a. Write an exponential function that represents the population.
y=
b. Find the population after 5 days.
There are
bacteria after 5 days.

Sagot :

fichoh

Answer:

y = 5e^1.9459101t

y = 84035

Step-by-step explanation:

Given the data:

X _____ Y

0 _____ 5

1 _____ 35

2 ____245

3 ____1715

4 __ 12005

Exponential function for the distribution :

y = initial(1 + rate)^t

y = Pe^rt

35 = 5e^r

35/5 = e^r

7 = e^r

Take In of both sides

1.9459101 = r

y = Pe^rt

y = 5e^1.9459101t

Population after 5 days :

y = 5e^1.9459101 * 5

y = 5e^9.7295505

y = 5 * 16806.995

y =84034.979

y = 84035

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